Quantum theory of surface-enhanced resonant Raman scattering (SERRS) of molecules in strongly coupled plasmon–exciton systems

Localised surface plasmons can couple strongly with the electronic transitions of a molecule, inducing new hybridised states of light and matter, the plasmon–exciton polaritons. Furthermore, molecules support vibrational degrees of freedom that interact with the electronic levels, giving rise to inelastic resonant Raman scattering under coherent laser illumination. Here we show the influence of strong plasmon–exciton coupling on resonant Raman processes that populate the vibrational states of the molecule and that lead to the characteristic surface-enhanced Raman scattering spectra. We develop analytical expressions that give insight into these processes for the case of moderate illumination intensity, weak electron–vibration coupling and no dephasing. These expressions help us to elucidate the twofold role of plasmon–exciton polaritons to pump the system efficiently and to enhance the Raman emission. Our results show a close analogy with the optomechanical process described for off-resonant Raman scattering but with a difference in the resonant reservoir. We also use full numerical calculations to study the effects reaching beyond these approximations and discuss the interplay between the fluorescence background and the Raman lines. Our results allow for better understanding and exploitation of the strong coupling regime in vibrational pumping and in the surface-enhanced resonant Raman scattering signal.